Engineering Content

Mechanics of Materials

Syllabus

  1. Introduction, Physical Units, and Scaling Relationships
    • Introduction
    • Physical Units
    • Scaling Relationships for Bars, Shafts, and Beams
  2. Static Equilibrium (Review)
    • Free Body Diagrams
    • Static Form of Newton’s Second Law of Motion
    • Static Equilibrium for Bars (Axial Loading)
    • Static Equilibrium for Shafts (Torsional Loading)
    • Static Equilibrium of Beams (Transverse Loading)
    • Static Equilibrium of Beams
      • Method of Joints
      • Method of Sections
  3. Axial Loading
    • Bars as Springs – Hooke’s Law
    • Axially Loaded Bars in Series and Parallel
    • Indeterminate Axial Loading of Bars
  4. Stress and Strain
    • Normal Stress
    • Shear Stress
    • Normal Strain
    • Shear Strain
    • Stress Tensors
  5. Material Properties I
    • Tensile and Compressive Tests
    • Stress-Strain Relationships for Brittle and Ductile Materials
    • Elastic Modulus – Young’s Modulus – Hooke’s Law
    • Uniaxial Failure from Yielding (Yield Strength)
  6. Material Properties II
    • Ductility
    • Simplified Material Models
      • Linearly Elastic-Perfectly Plastic Model
      • Linearly Elastic-Linearly Plastic Strain Hardening
    • Safety Factor
    • Modulus of Resilience
    • Modulus of Toughness
    • Poisson’s Ratio
    • A General Approach to Solving Problems in Mechanics
  7. Normal Loading I
    • Volumetric Strain and Dilation
    • Bulk Modulus
    • Safety Factors
    • Distributed Axial Loading
  8. Normal Loading II
    • Thermal Strain and Stress
    • Finite Element Analysis
  9. Torsion I
    • Shear Strain
    • Shear Strain in Torsion
    • Shear Modulus and Shear Stress
    • Shear Stress in a Shaft/Rod
  10. Torsion II
    • Angle of Twist
    • Distributed Torque
    • Indeterminate Twisted Shafts
    • Torsional Loading – FEA
  11. Beams I
    • Shear Force-Bending Moment Relationships
  12. Beams II
    • Graphing Shear Forces and Bending Moments
  13. Beams III
    • Local Deformation of a Beam
    • Bending Moment-Bending Stress Relationships
    • Flexure Formula
  14. Beams IV
    • Average Shear Stress
    • Transverse Shear Stress
  15. Thin-walled Pressure Vessels
  16. Combined Loadings: Superposition of Loads and Stresses
  17. Plane Stress I
    • Equilibrium on Sliced Elements
    • Transformations
  18. Plane Stress II
    • In-plane, Max/Min Principal Stresses
    • In-plane, Maximum Shear Stress
  19. Plane Stress III
    • Mohr’s Circle
  20. Absolute Maximum Shear Stress
  21. Plane Strain
    • Transformations
    • Mohr’s Circle
    • Strain Gauges
  22. Failure Criteria I
    • Brittle Materials: Max Normal Stress
    • Ductile Materials: Maximum Shear Stress
  23. Failure Criteria II
    • Safety Factors
    • Brittle Materials: Modified Max Normal Stress (Mohr Criterion)
    • Ductile Materials: Maximum Distortion Energy (von Mises)
  24. Beams V: Deflection
    • Displacement across a Beam
    • Typical Beam Bending Conditions, Displacements, and Slopes
    • The Ways of the “Engineer”
  25. Beams VI – Superposition
    • Statically Indeterminate Beams
    • Superposition
    • Beams as Springs

LAB INFORMATION

MechMat – Tensile Testing Lab

Previous Materials
Tips for using Colab Ipython to solve problems in mechanics of materials with appropriate units.
Video describing how to use Colab Ipython as a Calculator and Tracker of Units for Mechanics of Materials.

Content for an undergraduate course in mechanics of materials with embedded videos.

Complementary textbooks include the following:
Mechanics of Materials, 9th, 10th, or 11th Edition, Hibbeler, 2014, 2017, or 2022.
An Introduction to the Mechanics of Solids, 2nd Edition, Crandall, Dahl, and Lardner, 1999.
Fundamentals of Machine Component Design, 5th Edition, Juvinall and Marshek, 2012.

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